Okay, we are tasked with adding 8059 and 177. Let's begin!

Step 1: We'll start by adding the digits 9 & 7 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 5 & 7 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 1 in column 3 and get 2.

Step 4: We'll start by adding the digits 8 & 0 in column 4 and get 8.

So, 8059 + 177 = 8236.

